Oh...the square root denesting trick fixes a few cases, but it doesn't allow algsys to solve
[x^2+y^2-a, (x-1/2)^2 + (y-1/2)^2-b] for x & y, for example.
To see the origin of the nested square roots, try solving [x^2+y^2-1, (x-1/2)^2 + (y-1/2)^2-1] using
defun ebaksubst (solnl lhsl)
(displa `((mequal) solnl ((mlist) , at solnl)))
(displa `((mequal) lhsl ((mlist) ,@(mapcar #'pdis lhsl))))
(print "-----")
(mapcar #'(lambda (s) (cadr (ratf ($radcan (mfuncall '$sqrtdenest ($substitute (cons '(mlist) solnl) (pdis s))))))) lhsl))
Algorithmically, the pure resultant method used by algsys might seem straight forward, but the expensive part is rejecting
the spurious solutions.
--Barton
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I think that sqrt denesting is a possibly expensive operation. How
expensive is it if there are no square roots? In fact, there are no nested sqrts in this
expression, so it should not be necessary even here.